Group #36443820 — subgroups

Subgroups — #36443820

Order 22784.

802 conjugacy classes of subgroups; only the 243 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 243 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#13083557	C₂	1	3	yes	maximal
2	#26018079	C₂	1	3	yes	maximal, complemented
3	C₈₉×#1273	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13083557	C₄	1	6	yes	—
5	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
6	C₄×#13083557	—	2	12	no	—
7	C₂×#15667922	C₄	1	6	yes	—
8	C₂×C₄×#10623494	C₂²	1	3	yes	—
9	C₂×C₄×C₈×C₈₉	C₂²	1	3	yes	—
10	C₂²×C₄×D₈₉	C₂×C₄	1	3	yes	—
11	C₂×#13083557	—	2	12	no	—
12	C₂×#13083557	—	2	12	no	—
13	C₂×#13083557	—	2	12	no	—
14	C₂²×#10623494	C₂×C₄	1	6	yes	—
15	C₂×C₄×Dic₈₉	C₂×C₄	1	3	yes	—
16	C₄²×D₈₉	D₄	1	6	yes	—
17	C₄²×D₈₉	Q₈	1	2	yes	—
18	#15667922	—	2	12	no	—
19	C₄×#10623494	—	2	6	no	—
20	C₂²×C₈×C₈₉	C₂×C₄	1	6	yes	—
21	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
22	C₄×C₈×C₈₉	—	2	6	no	—
23	C₂³×D₈₉	C₄²	1	1	yes	characteristic
24	C₂²×Dic₈₉	C₄²	1	3	yes	—
25	C₂×C₄×D₈₉	—	2	6	no	—
26	C₂×C₄×D₈₉	—	2	6	no	—
27	C₂×C₄×D₈₉	C₂²⋊C₄	1	6	yes	—
28	C₂×C₄×D₈₉	C₄⋊C₄	1	6	yes	—
29	#13083557	—	2	48	no	—
30	C₂×#10623494	—	2	6	no	—
31	C₂×#10623494	—	2	6	no	—
32	C₂×#10623494	M₁₆	1	12	yes	complemented
33	C₄×Dic₈₉	C₂²⋊C₄	1	6	yes	—
34	C₄×Dic₈₉	C₄⋊C₄	1	6	yes	—
35	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
36	C₂×C₈×C₈₉	—	2	6	no	—
37	C₂×C₈×C₈₉	—	2	6	no	—
38	C₂×C₈×C₈₉	M₁₆	1	12	yes	complemented
39	C₄²×C₈₉	C₂×D₄	1	3	yes	—
40	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
41	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
42	C₂²×D₈₉	—	2	3	no	—
43	C₂²×D₈₉	—	2	3	no	—
44	C₂²×D₈₉	#95	1	2	yes	—
45	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	3	yes	—
46	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	3	yes	—
47	C₂×C₄×C₈₉	C₂×M₁₆	1	6	yes	—
48	C₂×C₄×C₈₉	C₂×M₁₆	1	6	yes	—
49	C₂×Dic₈₉	—	2	3	no	—
50	C₂×Dic₈₉	—	2	3	no	—
51	C₂×Dic₈₉	#95	1	6	yes	—
52	C₄×D₈₉	—	2	12	no	—
53	C₄×D₈₉	—	2	12	no	—
54	C₈×C₈₉	—	2	12	no	—
55	#10623494	—	2	12	no	—
56	C₂²×C₈₉	C₂×#95	1	1	yes	characteristic
57	C₂²×C₈₉	C₄×M₁₆	1	3	yes	—
58	C₂²×C₈₉	C₄×M₁₆	1	3	yes	—
59	C₂×D₈₉	—	2	6	no	—
60	C₂×D₈₉	—	4	1	no	—
61	C₂×D₈₉	—	4	3	no	—
62	C₄×C₈₉	#407	1	6	yes	—
63	C₄×C₈₉	#423	1	6	yes	—
64	Dic₈₉	—	2	6	no	—
65	#7852	—	89	1	no	maximal, Sylow
66	C₂×C₈₉	#1455	1	1	yes	characteristic
67	C₂×C₈₉	#1455	1	3	yes	—
68	C₂×C₈₉	#1728	1	3	yes	—
69	D₈₉	—	4	2	no	—
70	C₂×C₄×M₁₆	—	89	3	no	—
71	#1273	—	89	3	no	—
72	#1273	D₈₉	1	1	yes	characteristic, complemented
73	C₈₉	#7852	1	1	yes	characteristic, complemented, Sylow
74	C₂²×M₁₆	—	89	6	no	—
75	C₂²×C₄²	—	89	1	no	—
76	C₄×M₁₆	—	178	12	no	—
77	C₂×#97	—	89	6	no	—
78	C₂×C₄×C₈	—	89	3	no	—
79	C₂×C₄×C₈	C₂×D₈₉	1	3	yes	—
80	C₂³×C₄	—	89	3	no	—
81	C₂×M₁₆	—	178	12	no	—
82	C₂×M₁₆	—	178	12	no	—
83	C₂×M₁₆	—	178	12	no	—
84	C₂²×C₈	—	89	6	no	—
85	C₂²×C₈	C₄×D₈₉	1	6	yes	—
86	C₂×C₄²	—	89	3	no	—
87	C₂×C₄²	—	89	6	no	—
88	C₂×C₄²	—	89	2	no	—
89	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
90	#97	—	178	12	no	—
91	C₄×C₈	—	2	6	no	—
92	C₄×C₈	—	178	6	no	—
93	C₂⁴	—	89	1	no	—
94	C₂²×C₄	—	89	3	no	—
95	C₂²×C₄	—	89	6	no	—
96	C₂²×C₄	—	89	6	no	—
97	C₂²×C₄	—	178	6	no	—
98	C₂²×C₄	—	178	6	no	—
99	C₂²×C₄	C₂×C₄×D₈₉	1	3	yes	—
100	M₁₆	—	178	48	no	—
101	C₂×C₈	—	2	6	no	—
102	C₂×C₈	—	2	6	no	—
103	C₂×C₈	—	89	12	no	—
104	C₂×C₈	—	178	6	no	—
105	C₂×C₈	—	178	6	no	—
106	C₂×C₈	#13083557	1	12	yes	complemented
107	C₄²	—	89	6	no	—
108	C₄²	—	89	6	no	—
109	C₄²	D₄×D₈₉	1	3	yes	—
110	C₄²	Q₈×D₈₉	1	1	yes	characteristic
111	C₂³	—	89	2	no	—
112	C₂³	—	178	3	no	—
113	C₂³	—	178	3	no	—
114	C₂³	C₄²×D₈₉	1	1	yes	characteristic
115	C₂×C₄	—	89	6	no	—
116	C₂×C₄	—	178	3	no	—
117	C₂×C₄	—	178	3	no	—
118	C₂×C₄	—	178	12	no	—
119	C₂×C₄	—	178	12	no	—
120	C₂×C₄	C₂²⋊C₄×D₈₉	1	3	yes	—
121	C₂×C₄	C₄⋊C₄×D₈₉	1	3	yes	—
122	C₂×C₄	M₁₆×D₈₉	1	6	yes	—
123	C₂×C₄	C₂×#13083557	1	6	yes	—
124	C₈	—	2	12	no	—
125	C₈	—	178	12	no	—
126	C₂²	—	356	1	no	—
127	C₂²	—	356	3	no	—
128	C₂²	—	178	6	no	—
129	C₂²	#95×D₈₉	1	1	yes	characteristic
130	C₂²	C₄×#13083557	1	3	yes	—
131	C₂²	#19151550	1	3	yes	—
132	C₄	—	178	6	no	—
133	C₄	#19151560	1	6	yes	—
134	C₄	#19151620	1	6	yes	—
135	C₂	—	356	2	no	—
136	C₂	#26018554	1	1	yes	characteristic
137	C₂	#26018556	1	3	yes	—
138	C₂	#26019944	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×#13083557

C₂

yes

maximal

#26018079

C₂

yes

maximal, complemented

C₈₉×#1273

C₂

yes

maximal, characteristic, complemented

C₂²×#13083557

C₄

yes

—

C₂×C₄²×D₈₉

C₂²

yes

characteristic

C₄×#13083557

—

C₂×#15667922

C₄

yes

—

C₂×C₄×#10623494

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

—

C₂²×C₄×D₈₉

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×C₄×Dic₈₉

C₂×C₄

yes

—

C₄²×D₈₉

D₄

yes

—

C₄²×D₈₉

Q₈

yes

—

#15667922

—

C₄×#10623494

—

C₂²×C₈×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄×C₈×C₈₉

—

C₂³×D₈₉

C₄²

yes

characteristic

C₂²×Dic₈₉

C₄²

yes

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

C₂²⋊C₄

yes

—

C₂×C₄×D₈₉

C₄⋊C₄

yes

—

—

—

—

M₁₆

yes

complemented

C₄×Dic₈₉

C₂²⋊C₄

yes

—

C₄×Dic₈₉

C₄⋊C₄

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

M₁₆

yes

complemented

C₄²×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

C₂×Q₈

yes

characteristic

C₂³×C₈₉

C₂×C₄²

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

#95

yes

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₈₉

C₂×M₁₆

yes

—

C₂×C₄×C₈₉

C₂×M₁₆

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

#95

yes

—

C₄×D₈₉

—

C₄×D₈₉

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

C₂×#95

yes

characteristic

C₂²×C₈₉

C₄×M₁₆

yes

—

C₂²×C₈₉

C₄×M₁₆

yes

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₄×C₈₉

#407

yes

—

C₄×C₈₉

#423

yes

—

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₂×C₈₉

#1728

yes

—

D₈₉

—

C₂×C₄×M₁₆

—

#1273

—

#1273

D₈₉

yes

characteristic, complemented

C₈₉

#7852

yes

characteristic, complemented, Sylow

C₂²×M₁₆

—

C₂²×C₄²

—

C₄×M₁₆

—

178

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₈₉

yes

—

C₂³×C₄

—

C₂×M₁₆

—

178

—

C₂×M₁₆

—

178

—

C₂×M₁₆

—

178

—

C₂²×C₈

—

C₂²×C₈

C₄×D₈₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₈₉

yes

characteristic

#97

—

178

—

C₄×C₈

—

C₄×C₈

—

178

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

178

—

C₂²×C₄

—

178

—

C₂²×C₄

C₂×C₄×D₈₉

yes

—

100

M₁₆

—

178

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

178

—

105

C₂×C₈

—

178

—

106

C₂×C₈

#13083557

yes

complemented

107

C₄²

—

108

C₄²

—

109

C₄²

D₄×D₈₉

yes

—

110

C₄²

Q₈×D₈₉

yes

characteristic

111

C₂³

—

112

C₂³

—

178

—

113

C₂³

—

178

—

114

C₂³

C₄²×D₈₉

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

178

—

117

C₂×C₄

—

178

—

118

C₂×C₄

—

178

—

119

C₂×C₄

—

178

—

120

C₂×C₄

C₂²⋊C₄×D₈₉

yes

—

121

C₂×C₄

C₄⋊C₄×D₈₉

yes

—

122

C₂×C₄

M₁₆×D₈₉

yes

—

123

C₂×C₄

C₂×#13083557

yes

—

124

C₈

—

125

C₈

—

178

—

126

C₂²

—

356

—

127

C₂²

—

356

—

128

C₂²

—

178

—

129

C₂²

#95×D₈₉

yes

characteristic

130

C₂²

C₄×#13083557

yes

—

131

C₂²

#19151550

yes

—

132

C₄

—

178

—

133

C₄

#19151560

yes

—

134

C₄

#19151620

yes

—

135

C₂

—

356

—

136

C₂

#26018554

yes

characteristic

137

C₂

#26018556

yes

—

138

C₂

#26019944

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₈₉
commutator, socle	C₂³×C₈₉	C₂×C₄²
Fitting	C₈₉×#1273	C₂
prime radical	C₂³×D₈₉	C₄²
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1273	D₈₉
hypocenter	C₈₉	#7852
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₈₉

commutator, socle

C₂³×C₈₉

C₂×C₄²

Fitting

C₈₉×#1273

C₂

prime radical

C₂³×D₈₉

C₄²

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂³×C₈₉ ▷ C₈₉

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
2. #26018079	C₂	semidirect
3. C₈₉×#1273	C₂	semidirect
32. C₂×#10623494	M₁₆	semidirect
38. C₂×C₈×C₈₉	M₁₆	semidirect
72. #1273	D₈₉	semidirect
73. C₈₉	#7852	semidirect
106. C₂×C₈	#13083557	semidirect

H ≅ G/N

type

2. #26018079

C₂

semidirect

3. C₈₉×#1273

C₂

semidirect

32. C₂×#10623494

M₁₆

semidirect

38. C₂×C₈×C₈₉

M₁₆

semidirect

72. #1273

D₈₉

semidirect

73. C₈₉

#7852

semidirect

106. C₂×C₈

#13083557

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×#13083557	2
#26018079	2
C₈₉×#1273	2
#7852	89

subgroup

index

C₂×C₄×#13083557

#26018079

C₈₉×#1273

#7852

Subgroups — #36443820

Conjugacy classes of subgroups

Complements

Maximal subgroups